On complexity of Ehrenfeucht-Fraisse games

In this paper, we initiate the study of Ehrenfeucht-Fraisse games for some standard finite structures. Examples of such standard structures are equivalence relations, trees, unary relation structures, Boolean algebras, and some of their natural expansions. The paper concerns the following question that we call the Ehrenfeucht-Fraisse problem. Given n is an element of omega as a parameter, and two relational structures A and B from one of the classes of structures mentioned above, how efficient is it to decide if Duplicator wins the n-round EF game G(n)(A. B)? We provide algorithms for solving the Ehrenfeucht-Fraisse problem for the mentioned classes of structures. The running times of all the algorithms are bounded by constants. We obtain the Values of these constants as functions of n. (C) 2009 Elsevier B.V. All rights reserved.